こんにちは いぶきさん!

10 english questions!!!! I am happy to correct your japanese too!

Could you please correct my grammar??

1. I called on one of my friends in Quebec.

This is correct and means you visited them. You could also say, "I visited one of my friends in Quebec." If you meant you called them on the phone, you would say, "I called one of my friends in Quebec."

2. What's the difference between

yesterday, I ran across Dave in the city.

It sounds a little funny. If you were driving a car over Dave's body you might say this.

yesterday, I ran into in to Dave in the city.

Into means inside of. I ran into (inside) the restaurant. You mean, "you ran in to Dave." I would put yesterday at the end. How you have it is ok, but it is smoother like, "I ran in to Dave in the city, yesterday."

3. If I put this poem into Japanese, I it will be little strange. 

I would write it like this, "If I write this poem in Japanese, it will look (or sound) a little strange."

4. There are some people who counter my opinion.

This is technically correct. However we would say, "There are some people who disagree with me."

5. There was a considerable rise of the birthrate in 1990.

Good. "rise in the birthrate" might be a little more common.

6. He always lags behind in his work.

7. The civil war in South Africa arose from the religion.

You could remove 'the'. It really depends on the context.

8. As my grandma has to take care of my grandpa all the time, he is a burden for her.

It is correct, but it would be smoother like this. "My grandpa is a burden for my grandma since she has to take care of him all the time."

9. If you just only smile when you don't understand what others say are saying, you imply that you didn't understood understand everything.

Blue words are more natural choices. Red are corrections.

10. Teachers at schools always impose their rules on pupils.

If you are talking about teachers in general and schools in general, you need an s at the end of schools. If you are talking about a specific school and specific teachers, like a school we both go to, then you could say, "The teachers at school".

じゃまた！